Comparative study of the three frequent encountered numerical methods of integration with emphasis on their error terms

Very few functions can be integrated analytically. For the large class of those ones whose integral cannot be found such a way, only numerical methods are helpful. They are many and all of them generate errors. The goal of this paper is to find out those ones which minimize these errors. The most encountered numerical methods the Newton-Cotes, Tchebyshev and Gauss. This study indicates that the method of Gauss gives better results, follows by the method of Tchebyshev. The method of Newton-Cotes is at the third position. Moreover, for more accurate results the integrating function should be replace by an algebraic function of order not exceeding 2.